The crisis in Britain's relationship with continental Europe won't be resolved unless it is understood, and that is easier said than done. At first sight, David Cameron's petulance at the Brussels summit was merely the latest chapter in a 60-year-old story. Euroscepticism has been constant in British politics since the Attlee government turned down membership of the European Coal and Steel Community because the Durham miners wouldn't wear it.

But scepticism has morphed into phobia. There is a raw virulence about today's anti-European rhetoric. It is visceral, not intellectual; it comes from the gut, not the head. It draws on a deep, existential anxiety that no policy changes could allay. If Europhobes got their way on repatriating powers, they would demand withdrawal from the EU. If Britain withdrew, their rage would be unappeased. The "Brussels" they excoriate is a symbol of encroaching evil, a witches' coven of malice and spite. Their rhetoric has nothing to do with policy; it is about identity and recognition.

Where does this anxiety come from? Whose identity is in question? I used to think it was a post-imperial anxiety, rather like that of Putin's Russia. Now I think it is far more complicated. The empire disappeared decades ago, when many of today's Europhobes were in short pants or not yet born. Besides, it was British. Europhobia is English. It was English Tory MPs who told Cameron to behave like a bulldog when he got to Brussels and who sizzled with hatred for the Lib Dems after his return. English red top papers have been stoking the fires of Europhobia ever since Margaret Thatcher's defenestration. Indeed the Tory party itself is now an English party, not a British one.

The crisis in Britain's relationship with mainland Europe has its roots in a peculiarly English identity crisis with no counterpart north of the border or west of the Severn. The Scots and Welsh know who they are. For centuries, they have had two identities – their own, and a wider British one. They are unfazed by the discovery of a third European identity as well. They are at home in Europe, where multiple identities are becoming the norm. To them, it seems only right that Europe's once monolithic sovereign states now have to share power, both with a supranational union and with rediscovered nations, principalities and provinces within their borders. Along with Catalans, Basques, Flemings, Walloons, Corsicans, Sardinians and even Bretons, the Scots and Welsh are emerging from a homogenising central state of the recent past.

Like their continental counterparts they can draw on wells of memory and myth to craft a narrative of Europeanness. In Scotland's case, the well is deep. Before the 1707 Act of Union Scotland was an independent European state, with its own monarch, parliament, church and legal system. The fact that its monarch was also monarch of England did not detract from that status. In the middle ages, Scotland was allied with France against England, while heroes like William Wallace and Robert the Bruce fought for Scottish freedom. In the 16th century it embraced a stark, Calvinist Protestantism that hailed from Geneva, and differed profoundly from the middle way of the Church of England. Scottish independence would be a restoration, not a revolution. It would enable Scotland to resume an honoured place in the European journey.

The Welsh well is not as deep as that, but it is deep enough for its explorers to see themselves as an ancient European people with continental links that long antedate the Anglo-Saxon conquest. None of this is true of England. It too was a European kingdom before it merged with Scotland, and had close links with the continent. But the English myth is one of heroic separation from the mainland, not engagement with it: of England as a providential nation summoned by a higher power to defend freedom from continental assault.

The English doctrine of absolute parliamentary sovereignty runs against the grain of the rediscovered provincialism of modern Europe. Above all, the English of the 21st century no longer know who they are. They used to think that "English" and "British" were synonymous. Now they know that they are not. But they don't know how Englishness and Britishness relate to each other, and they can't get used to the notion of multiple identities. Until they do, I don't see how the crisis in Britain's relationship with continental Europe can be resolved. If it isn't, the most likely prospect is of further European political union and the break-up of the UK, with England staying out and Scotland and Wales going in.